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<div  id='write'  class = 'is-node show-fences-line-number'><h1><a name='header-n0' class='md-header-anchor '></a>Ceres Learning</h1><p><a href='https://github.com/Ling-Bao/Ceres_Learning'>githut</a></p><h2><a name='header-n4' class='md-header-anchor '></a>0 参考资料</h2><p>（1）<a href='http://www.ceres-solver.org/index.html'>Ceres Solver</a></p><p>（2）<a href='http://blog.csdn.net/huajun998/article/details/76136710'>Ceres-Solver学习笔记(1)</a></p><p>（3）<a href='http://blog.csdn.net/huajun998/article/details/76145441'>Ceres-Solver学习笔记(2)</a></p><p>（4）<a href='http://blog.csdn.net/huajun998/article/details/76165511'>Ceres-Solver学习笔记(3)</a></p><p>（5）<a href='http://blog.csdn.net/huajun998/article/details/76166307'>Ceres-Solver学习笔记(4)</a></p><p>（6）<a href='http://blog.csdn.net/huajun998/article/details/76177592'>Ceres-Solver学习笔记(5)</a></p><p>（7）<a href='http://blog.csdn.net/huajun998/article/details/76222745'>Ceres-Solver学习笔记(6)</a></p><p>（8）<a href='http://blog.csdn.net/huajun998/article/details/76271938'>Ceres-Solver学习笔记(7)</a></p><p>（9）<a href='http://blog.csdn.net/huajun998/article/details/76341292'>Ceres-Solver学习笔记(8)</a></p><p>（10）<a href='http://blog.csdn.net/huajun998/article/details/76423003'>Ceres-Solver学习笔记(9)</a></p><h2><a name='header-n25' class='md-header-anchor '></a>1 练练手</h2><h3><a name='header-n26' class='md-header-anchor '></a>1.1 非约束最优化问题</h3><p><span class="MathJax_Preview"></span><span class="MathJax_SVG_Display"><span class="MathJax_SVG" id="MathJax-Element-24-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="93.385ex" height="5.145ex" viewBox="0 -1359 40207.4 2215.4" role="img" focusable="false" style="vertical-align: -1.777ex; margin-bottom: -0.212ex;"><defs><path stroke-width="1" id="E25-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 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。</p><p>​	（3.2）编写CostFunction结构体。</p><p>​	（3.3）构造一个求解非线性最小二乘法的Problem来进行未知数求解。</p><p><strong>（4）总结</strong></p><p>​	（4.1）利用ceres无法对非线性函数进行曲线拟合，如魏尔斯特拉斯函数。原因包括两点：函数无法进行微分求解和初始点难以选取。</p><p>​	（4.2）此处改为ceres对<span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-7-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.109ex" height="3.044ex" viewBox="0 -1007.2 4352.4 1310.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="1" id="E8-MJMATHI-79" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 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x="607" y="-213"></use></g><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-28" x="6315" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-59" x="6705" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-2212" x="7468" y="0"></use><g transform="translate(5831,0)"><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-59" x="0" y="0"></use><use transform="scale(0.5)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-73" x="822" y="-213"></use></g><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-29" x="9260" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-2B" x="9650" y="0"></use><g transform="translate(7374,0)"><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-63" x="0" y="0"></use><use transform="scale(0.5)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-32" x="613" y="-213"></use></g><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-28" x="11316" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-5A" x="11705" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-2212" x="12429" y="0"></use><g transform="translate(9339,0)"><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-5A" x="0" y="0"></use><use transform="scale(0.5)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-73" x="966" y="-213"></use></g><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-29" x="14323" y="0"></use></g><g transform="translate(60,-436)"><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-61" x="0" y="0"></use><use transform="scale(0.5)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-33" x="748" y="-213"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-28" x="983" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-58" x="1372" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-2212" x="2225" y="0"></use><g transform="translate(2124,0)"><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-58" x="0" y="0"></use><use transform="scale(0.5)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-73" x="1171" y="-213"></use></g><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-29" x="4264" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-2B" x="4653" y="0"></use><g transform="translate(3841,0)"><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-62" x="0" y="0"></use><use transform="scale(0.5)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-33" x="607" y="-213"></use></g><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-28" x="6315" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-59" x="6705" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-2212" x="7468" y="0"></use><g transform="translate(5831,0)"><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-59" x="0" y="0"></use><use transform="scale(0.5)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-73" x="822" y="-213"></use></g><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-29" x="9260" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-2B" x="9650" y="0"></use><g transform="translate(7374,0)"><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-63" x="0" y="0"></use><use transform="scale(0.5)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-33" x="613" y="-213"></use></g><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-28" x="11316" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-5A" x="11705" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-2212" x="12429" y="0"></use><g transform="translate(9339,0)"><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-5A" x="0" y="0"></use><use transform="scale(0.5)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMATHI-73" x="966" y="-213"></use></g><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E32-MJMAIN-29" x="14323" y="0"></use></g></g></g></g></g></g></g></g></g></g></g></svg></span></span><script type="math/tex; mode=display" id="MathJax-Element-29">\begin{equation} \begin{split} \left\{ \begin{array}{} x-x_{0}=- f\frac{a_{1}(X-X_{s})+b_{1}(Y-Y_{s})+c_{1}(Z-Z_{s})}{a_{3}(X-X_{s})+b_{3}(Y-Y_{s})+c_{3}(Z-Z_{s})}, & \\ y-y_{0}=-f \frac{a_{2}(X-X_{s})+b_{2}(Y-Y_{s})+c_{2}(Z-Z_{s})}{a_{3}(X-X_{s})+b_{3}(Y-Y_{s})+c_{3}(Z-Z_{s})} \end{array}  \right. \end{split} \tag{3} \end{equation}</script></p><p>​	其中<span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-10-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.924ex" height="2.577ex" viewBox="0 -806.1 3411.6 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="1" id="E11-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="1" id="E11-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="1" id="E11-MJMAIN-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path stroke-width="1" id="E11-MJMATHI-79" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path stroke-width="1" id="E11-MJMATHI-66" d="M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E11-MJMATHI-78" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E11-MJMAIN-30" x="809" y="-213"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E11-MJMAIN-2C" x="1026" y="0"></use><g transform="translate(1471,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E11-MJMATHI-79" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E11-MJMAIN-30" x="693" y="-213"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E11-MJMAIN-2C" x="2415" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E11-MJMATHI-66" x="2861" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-10">x_{0}, y_{0}, f</script>已知，<span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-11-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.234ex" height="1.994ex" viewBox="0 -755.9 1392.5 858.4" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="1" id="E12-MJMATHI-61" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path><path stroke-width="1" id="E12-MJMATHI-62" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path><path stroke-width="1" id="E12-MJMATHI-63" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E12-MJMATHI-61" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E12-MJMATHI-62" x="529" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E12-MJMATHI-63" x="959" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-11">abc</script>为旋转矩阵，可以利用<span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-12-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.238ex" height="2.461ex" viewBox="0 -755.9 2685.8 1059.4" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="1" id="E13-MJMATHI-3D5" d="M409 688Q413 694 421 694H429H442Q448 688 448 686Q448 679 418 563Q411 535 404 504T392 458L388 442Q388 441 397 441T429 435T477 418Q521 397 550 357T579 260T548 151T471 65T374 11T279 -10H275L251 -105Q245 -128 238 -160Q230 -192 227 -198T215 -205H209Q189 -205 189 -198Q189 -193 211 -103L234 -11Q234 -10 226 -10Q221 -10 206 -8T161 6T107 36T62 89T43 171Q43 231 76 284T157 370T254 422T342 441Q347 441 348 445L378 567Q409 686 409 688ZM122 150Q122 116 134 91T167 53T203 35T237 27H244L337 404Q333 404 326 403T297 395T255 379T211 350T170 304Q152 276 137 237Q122 191 122 150ZM500 282Q500 320 484 347T444 385T405 400T381 404H378L332 217L284 29Q284 27 285 27Q293 27 317 33T357 47Q400 66 431 100T475 170T494 234T500 282Z"></path><path stroke-width="1" id="E13-MJMAIN-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path stroke-width="1" id="E13-MJMATHI-3C9" d="M495 384Q495 406 514 424T555 443Q574 443 589 425T604 364Q604 334 592 278T555 155T483 38T377 -11Q297 -11 267 66Q266 68 260 61Q201 -11 125 -11Q15 -11 15 139Q15 230 56 325T123 434Q135 441 147 436Q160 429 160 418Q160 406 140 379T94 306T62 208Q61 202 61 187Q61 124 85 100T143 76Q201 76 245 129L253 137V156Q258 297 317 297Q348 297 348 261Q348 243 338 213T318 158L308 135Q309 133 310 129T318 115T334 97T358 83T393 76Q456 76 501 148T546 274Q546 305 533 325T508 357T495 384Z"></path><path stroke-width="1" id="E13-MJMATHI-3BA" d="M83 -11Q70 -11 62 -4T51 8T49 17Q49 30 96 217T147 414Q160 442 193 442Q205 441 213 435T223 422T225 412Q225 401 208 337L192 270Q193 269 208 277T235 292Q252 304 306 349T396 412T467 431Q489 431 500 420T512 391Q512 366 494 347T449 327Q430 327 418 338T405 368Q405 370 407 380L397 375Q368 360 315 315L253 266L240 257H245Q262 257 300 251T366 230Q422 203 422 150Q422 140 417 114T411 67Q411 26 437 26Q484 26 513 137Q516 149 519 151T535 153Q554 153 554 144Q554 121 527 64T457 -7Q447 -10 431 -10Q386 -10 360 17T333 90Q333 108 336 122T339 146Q339 170 320 186T271 209T222 218T185 221H180L155 122Q129 22 126 16Q113 -11 83 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transform="translate(23713,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E38-MJMAIN-28" x="0" y="0"></use><g transform="translate(389,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E38-MJMATHI-78" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E38-MJMAIN-31" x="809" y="-213"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E38-MJMAIN-2212" x="1638" y="0"></use><g transform="translate(2638,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E38-MJMATHI-78" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E38-MJMAIN-34" x="809" y="-213"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E38-MJMAIN-29" x="3665" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E38-MJMAIN-34" x="5734" y="675"></use></g></g></g></g></g></svg></span></span><script type="math/tex; mode=display" id="MathJax-Element-33">f(X)=\left(x_1+10x_2\right)^2+5\left(x_3-x_4\right)^2+\left(x_2-2x_3\right)^4+10\left(x_1-x_4\right)^4 \tag{5}</script></p><p>	其中：</p><p>​	<span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-18-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="29.665ex" height="2.344ex" viewBox="0 -755.9 12772.6 1009.2" role="img" focusable="false" style="vertical-align: -0.588ex;"><defs><path stroke-width="1" id="E19-MJMAIN-2219" d="M55 251Q55 328 112 386T249 444T386 388T444 249Q444 171 388 113T250 55Q170 55 113 112T55 251Z"></path><path stroke-width="1" id="E19-MJMAIN-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path stroke-width="1" id="E19-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 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xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E19-MJMAIN-2C" x="10881" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E19-MJMAIN-33" x="11326" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E19-MJMAIN-2C" x="11826" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E19-MJMAIN-34" x="12272" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-18">\bullet -10\leq x_i\leq 10, i=1,2,3,4</script></p><p>​	<span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-19-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="14.652ex" height="2.577ex" viewBox="0 -806.1 6308.3 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="1" id="E20-MJMAIN-2219" d="M55 251Q55 328 112 386T249 444T386 388T444 249Q444 171 388 113T250 55Q170 55 113 112T55 251Z"></path><path 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336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path stroke-width="1" id="E20-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 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x="5807" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-19">\bullet f_{min}(X^*)=0</script></p><p>​	<span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-20-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.807ex" height="2.694ex" viewBox="0 -755.9 3361.5 1160" role="img" focusable="false" style="vertical-align: -0.938ex;"><defs><path stroke-width="1" id="E21-MJMAIN-2219" d="M55 251Q55 328 112 386T249 444T386 388T444 249Q444 171 388 113T250 55Q170 55 113 112T55 251Z"></path><path stroke-width="1" id="E21-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 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href='http://blog.sciencenet.cn/blog-3276147-1030202.html'>ceres solver学习之bundle adjustment</a></p><p><img src='picture/BA_ProjectionError.png' alt='Bundle Adjustment Projection Error' /></p><p><strong>（3）步骤</strong></p><p>​	（3.1）读取<strong>problem-49-7776-pre.txt.bz2</strong>数据。</p><p>​	（3.2）编写CostFunction结构体。</p><p>​	（3.3）构造一个求解非线性最小二乘法的Problem来进行未知数求解。</p><p><strong>（4）运行结果</strong></p><p><img src='picture/BA_SolveResult.png' alt='Simple Bundle Adjustment Solve Result' /></p><p></p></div>
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